The install package or script should have documentation or a command line option specifyign where it installs the new version of Python. Simply add that to your $PATH environment variable -- in bash, this is done via:
If a special lbirary directory is needed, you might need to add it to your $LD_LIBRARY_PATH in a similar fashion.
You might want to read some basic documentation on the bash shell (command interpreter). If you're new to Cygwin and *nix-like environments, it will help you a lot.